A photonic analog-to-digital converter based on an unbalanced Mach-Zehnder quantizer

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1 A photonic analog-to-digital converter based on an unbalanced Mach-Zehnder quantizer Chris H. Sarantos and Nadir Dagli* Department of Electrical Engineering, University of California Santa Barbara, CA, 936, USA Abstract: A Mach-Zehnder modulator (MZM) based analog to digital converter (ADC) is described. The signal to be digitized is applied to a single electrode of a high speed unbalanced modulator that acts as a quantizer. The rest of the system consists of commercially available wavelength division multipling (WDM) components. Analysis indicates that 6 bit operation at 4 Giga Samples per second (GS/s) is possible with moderate optical carrier power. 2 Optical Society of America OCIS codes: (3.3) Integrated optics; (3.32 Integrated optics devices; (23.4) Modulators; (6.233) Fiber optics communications. References and links. F. Coppinger, A. Bhushan, and B. Jalali, Photonic time stretch and its application to analog-to-digital conversion, IEEE Trans. Microw. Theory Tech. 47(7), (999). 2. C. Xu, and X. Liu, Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters, Opt. Lett. 28(2), (23). 3. S. Oda, and A. Maruta, A Novel Quantization Scheme by Slicing Supercontinuum Spectrum for All-Optical Analog-to-Digital Conversion, IEEE Photon. Technol. Lett. 7(2), (25). 4. T. Nishitani, T. Konishi, and K. Itoh, Resolution Improvement of All-Optical Analog-to-Digital Conversion Employing Self-frequency Shift and Self-Phase-Modulation-Induced Spectral Compression, IEEE J. Sel. Top. Quantum Electron. 4(3), (28). 5. R. Pant, C. Xiong, S. Madden, B. L. Davies, and B. J. Eggleton, Investigation of all-optical analog-to-digital quantization using a chalcogenide waveguide: A step towards on-chip analog-to-digital conversion, Opt. Commun. 283(), (2). 6. Y. Miyoshi, S. Takagi, S. Namiki, and K. Kitayama, Multiperiod PM-NOLM With Dynamic Counter- Propagating Effects Compensation for 5-Bit All-Optical Analog-to-Digital Conversion and Its Performance Evaluations, J. Lightwave Technol. 28(4), (2). 7. B. Shoop, Photonic analog-to-digital conversion, (Springer-Verlag, 2). 8. C. Sarantos and N. Dagli, An Unbalanced MZM based Photonic Analog-to-Digital Converter, Proceedings of IEEE/LEOS 27 Annual Meeting, pp. -, Q. Wu, H. Zhang, Y. Peng, X. Fu, and M. Yao, 4GS/s Optical analog-to-digital conversion system and its improvement, Opt. Express 7(), (29).. E. A. J. Marcatili, Optical subpicosecond gate, Appl. Opt. 9(9), (98).. J. J. Veselka, and S. K. Korotky, Pulse Generation for Soliton Systems Using Lithium Niobate Modulators, IEEE J. Sel. Top. Quantum Electron. 2(2), 3 3 (996). 2. H. A. Haus, S. T. Kirsch, K. Mathyssek, and F. J. Leonberger, Picosecond optical sampling, IEEE J. Quantum Electron. 6(8), (98). 3. D. J. Bachmann, N. Dagli, J. Calusdian, P. E. Pace, and J. P. Powers, Optical Pulse Train Generation Using Modulator Cascades, Proceedings of IEEE/LEOS 28 Annual Meeting, Paper TuF-4, pp. 9 9, Newport Beach, CA, November 9 3, N. Dagli, Wide Bandwidth Lasers and Modulators for RF Photonics, IEEE Trans. Microw. Theory Tech. 47(7), 5 7 (999). 5. K. M. Noguchi, and H. Miyazawa, Design of Ultra Broad Band LiNbO 3 Optical Modulators with Ridge Structure, IEEE Trans. Microw. Theory Tech. MTT-43, (995). 6. J. H. Shin, S. Wu, and N. Dagli, 35 GHz Bandwidth, 5 V-cm Drive Voltage, Bulk GaAs Substrate Removed Electro Optic Modulators, IEEE Photon. Technol. Lett. 9(8), (27). 7. Y. Miyamoto, M. Yoneyama, Y. Imai, K. Kato, and H. Tsunetsugu, 4 Gbit/s optical receiver module using a flip-chip bonding technique for device interconnection, Electron. Lett. 34(5), (998). 8. G. Agrawal, Fiber Optic Communications Systems, Section 4.6., (Wiley, 997). # $5. USD Received 2 Apr 2; revised 2 Jun 2; accepted 2 Jun 2; published 23 Jun 2 (C) 2 OSA 5 July 2 / Vol. 8, No. 4 / OPTICS EXPRESS 4598

2 . Introduction Digital signal processing in applications such as radar, telecommunications and high speed instrumentation requires digitization of analog signals with both high sampling rate and high resolution. Photonic ADCs have been proposed to achieve high sampling rates. One approach uses a photonic time stretch preprocessor followed by an electronic ADC []. Other approaches use all optical techniques [2 6]. There are other approaches using optical modulators, but require either one modulator per bit or electronic signal distribution to many electrodes [7], offering limited ability to scale to high bandwidth, high resolution systems. Here, we describe a high bandwidth, high resolution ADC design based on a single wide bandwidth Mach-Zehnder modulator (MZM) [8,9] and commercially available components. 2. Device description Figure shows the schematic of the proposed ADC. The system consists of a multi wavelength continuous wave (CW) source, a quantizer, a demultipler, sampler(s) and receivers. Diode lasers operating at different wavelengths are multipled into a waveguide using an arrayed waveguide grating (AWG). The waveguide feeds into a high speed unbalanced MZM acting as a quantizer. The spectral channels are then demultipled and each is temporally sampled. Alternatively, all channels could be sampled with a single device before demultipling. There are several different sampling technologies in integrated optics suitable for sampling needed. They can be directional coupler or Mach-Zehnder based [ 3]. All these technologies enable sub picosecond sampling at very high repetition rates. The sampled outputs are detected and compared to a binary threshold. The outputs of the receivers form a digital code corresponding to the analog signal applied to the MZM electrode. The system is similar to a wavelength division multipled (WDM) transmission system without the transmission fiber. All components are either commercially available or require only slight modifications to commercial designs. λ λ λ 2 λ 2 λ 4 MUX V s ~ Z L DE MUX λ 4 λ 5 λ 5 Quantizer (Unbalanced high speed modulator) High speed samplers λ N λ N CW Sources Receivers Fig.. Schematic of the proposed ADC. CW sources are multipled and fed into an unbalanced MZM, where an analog input voltage modulates the spectral channels simultaneously. The channels are then demultipled, temporally sampled and thresholded. The combined binary outputs of the thresholded channels form a digital representation of the applied voltage. An unbalanced MZM can quantize an applied voltage when its transfer function is applied to multiple wavelengths. The normalized output power as a function of drive voltage and wavelength is: P P out max cos πv π n L 2 s = + 2V π λ () where V S is the analog voltage to be quantized, V π is the voltage required to shift the relative phase of the interferometer arms by π, n the refractive ind, L the length difference between the interferometer arms and λ the free-space wavelength of the optical input. P max is the output power in the fully on state of the MZM. The output power varies sinusoidally with # $5. USD Received 2 Apr 2; revised 2 Jun 2; accepted 2 Jun 2; published 23 Jun 2 (C) 2 OSA 5 July 2 / Vol. 8, No. 4 / OPTICS EXPRESS 4599

3 applied voltage. The voltage independent term in the cosine argument depends plicitly on λ, shifting the sinusoid along the voltage axis as λ changes. Figure 2 shows the MZM output at four equally-spaced wavelengths as a function of input voltage. When the modulated channels are spectrally demultipled and detected using the same threshold level, a digital code differentiating the analog input voltage levels is generated as shown in Fig. 2. This code is known as a cyclic thermometer code. As the coded value increases, only one digit changes at a time, facilitating error correction [7]. The number of resolved values over a voltage range of 2V π is given by twice the number of input wavelengths ( 2N λ ). The minimum resolvable voltage is V Eq. (2) as π N. The code repeats for voltages over 2V λ π. The bits of resolution b is given ( ) b= + log 2 N λ (2) The electro-optic modulators used in this design allow for sampling rates beyond the capabilities of conventional electronics. MZMs with bandwidths ceeding 4 GHz and approaching GHz have been realized using several technologies [4 6]. Therefore this approach could be used to digitize signals with bandwidths in cess of 4 GHz. Transmission λ. Code.9 λ λ λ λ λ Normalized voltage V/V π Fig. 2. Transfer function of the unbalanced MZ modulator at different wavelengths as a function of normalized voltage. The thermometer-coded values at the top result from thresholding each channel at half the maximum power. 3. Results and discussion This section investigates the required power levels out of the sources. The analysis is very similar to the analysis of a high speed fiber optic system. We assume that the samplers provide a Gaussian shaped time-gate with full width at half maximum (FWHM) of τ seconds at a sampling rate of B= / T samples per second. Figure 3(a) shows the received pulses at a certain wavelength. The detection threshold level is P. Because of noise and other impairments there is a certain region between P and P around P th that cannot be clearly described as either above or below the threshold. Pulses with amplitudes higher than P or lower than P are definitively labeled as a or, respectively. Using the transfer function of the quantizer at the specific wavelength one can convert the range from P to P to a voltage range Vmin as shown in Fig. 3(c). This will be the minimum voltage resolution that can be achieved. Any voltage swing less than Vmin will not generate enough power swing that will give a transition from a to a or vice versa, hence cannot be resolved. Furthermore the phase shift of the transfer function for adjacent wavelengths should be such that as one wavelength makes a transition from to adjacent wavelengths should definitely be or as illustrated in Fig. 3(c). This condition determines the minimum phase shift between transfer function at different wavelengths or λ. This in turn determines L for a given λ as th Threshold level # $5. USD Received 2 Apr 2; revised 2 Jun 2; accepted 2 Jun 2; published 23 Jun 2 (C) 2 OSA 5 July 2 / Vol. 8, No. 4 / OPTICS EXPRESS 46

4 described earlier. The calculation of P and P can be done using fiber optic communication system analysis. For this purpose the model shown in Fig. 3(b) is used. We assume that input pulses will be received as either a or a. Our pulse train is equivalent to a return to zero (RZ) transmission with low tinction ratio and low duty cycle. The minimum P and maximum P levels that allow error-free operation of this transmission system will also allow error-free operation of the ADC. The least resolvable voltage, Vmin, can be calculated once these limits are found. Then, the maximum number of bits or resolution can be determined using the formula in Eq. (3) VFS b Vπ b Vπ = 2 = 2 b= log2 + (3) Vmin Vmin Vmin Fig. 3. (a) Schematic illustration of the pulses of certain wavelength before the receiver, (b) received pulses of a digital communication link having the same detection levels as the proposed ADC, (c) panded unbalanced MZM transfer function around P th for three different wavelengths. In this formulation it is assumed that V = 2. In a fiber optic transmission system error FS free operation is defined as operation with a bit error rate (BER) of 9 or less. For 4 Gb/s operation the average received power in a back to back RZ system with good tinction ratio τ / T = / 5 for 9 BER is about 23.5 dbm [7]. In such a RZ system and duty cycle of ( ) RZ the average power in terms of peak power is ( τ ) Pav = Ppeak / T = Ppeak / 5. P RZ peak is the unmodulated CW power output in the fully-on state of the MZM. It is usually assumed that the tinction ratio is really high so that P Ppeak and P. In the digital communication system that represents the ADC the average received power to a good approximation is P = P τ / T. Therefore to get the same average power for a good BER the peak ( ) av peak ADC power should be increased by a factor of P ( T / τ) /( T / τ) V π =. This is the power penalty av RZ ADC # $5. USD Received 2 Apr 2; revised 2 Jun 2; accepted 2 Jun 2; published 23 Jun 2 (C) 2 OSA 5 July 2 / Vol. 8, No. 4 / OPTICS EXPRESS 46

5 due to low duty cycle. Typical ( T / τ ) values are at the order of 25 and the corresponding ADC power penalty is about 7 db. In addition for good resolution P and P should be close to one another, i.e., tinction ratio should be low. Low tinction ratio introduces another power penalty, δ given in Eq. (4) as [8]. ( ) /( ) δ = P + P P P (4) The average power must be increased by this factor to match the BER of the system with P = P V and high tinction ratio. Using the transfer function of the quantizer out ( ) P = P ( V ), where V V = V = V π. Letting n L / ( m / 2) out Eq. (), we can press δ as: min / 2 b π λ = + π in 2 π V π 2 π V cos + cos b + 2 Vπ Vπ δ = (5) 2 π V π 2 π V cos + cos b 2 Vπ Vπ Using this formula and V = V π / 2 we estimate a power penalty of 3.5 db for 6 bit operation. Combining this penalty with the penalty of 7 db for low duty cycle we get a total penalty of 2.5 db. This is about the loss of 7 km of fiber. The ADC is therefore similar to a typical WDM communications link as far as power budgets are concerned. Error free operation requires a received peak power of about 3 dbm or.5 mw. Assuming a db insertion loss for the quantizer, sampler and two AWGs, the required input power per channel is about 5 mw. This power is readily achievable using conventional laser diodes. The temporal sampling method and parameters also affect ADC performance. According to a previous analysis of the proposed ADC based on signal-to-noise ratio calculations [8], the resolution and input power reported here are obtainable when sampling with a Gaussian aperture 5 ps wide (FWHM) and an rms jitter of.2 ps. The spectral spacing and MZM length offset are also feasible. The spectral spacing must be large enough to avoid spectral overlap, and small enough to avoid significant dispersion in V π that would lead to code nonlinearity. For a 2 GHz signal, the standard GHz ITU spacing should be sufficient. Sampling before demultipling increases each channel s bandwidth, requiring increased channel spacing This spectral spacing determines the required length offset L. For a given spectral grid, L determines the spacing between transfer functions at different wavelengths along the voltage axis. Equal spacing is achieved if the ϕ = 2m+ π 2 between two adjacent phase of the transfer function changes by ( ) channels separated in frequency by to Eq. (): ν, where m is an integer. Applying this condition ( 2 ) /( 2 ) L= c m+ nn λ ν (6) The voltage spacing between transfer functions must also be large enough to insure that only one channel at a time lies in the uncertain power region, as shown in Fig. 3. Choosing m to satisfy this condition leads to a L ~2 µm. This offset is readily achieved by varying the half angles of the y-branch splitters of the MZM, as shown in Fig.. Additionally, a DC biased section in one arm could fine-tune the phase offset and stabilize the MZM during operation. The source wavelengths may also drift. This increases N λ δ by shifting transfer functions δ increases with respect to each other. For a typical wavelength-locked diode drift of 5 pm, by less than db based on Eq. (5). Therefore the ADC is robust to wavelength drift. # $5. USD Received 2 Apr 2; revised 2 Jun 2; accepted 2 Jun 2; published 23 Jun 2 (C) 2 OSA 5 July 2 / Vol. 8, No. 4 / OPTICS EXPRESS 462

6 4. Conclusion We introduce a novel photonic ADC design that resembles a WDM digital link with an unbalanced MZM between the transmitters and receivers. We show that the required MZM fabrication and WDM spectral grid are well within the capabilities of isting technology. A reasonable optical source power is predicted to deliver 6 bits of resolution at 4 GS/s. Higher sampling rates ~ GS/s are possible due to the high bandwidth of MZMs. Acknowledgements This work was supported by National Science Foundation (NSF) Grant ECCS # $5. USD Received 2 Apr 2; revised 2 Jun 2; accepted 2 Jun 2; published 23 Jun 2 (C) 2 OSA 5 July 2 / Vol. 8, No. 4 / OPTICS EXPRESS 463